Introduction

What the chapter is about

• Direct current does not change direction with time. An alternating voltage varies sinusoidally with time and reverses its direction periodically; the current it drives in a circuit is the alternating current.
• The standard source used throughout: $v = v_m\sin\omega t$, with $v_m$ the amplitude (peak value) of the oscillating potential difference and $\omega = 2\pi\nu$ its angular frequency in rad s$^{-1}$.
• The domestic mains supply in India is an ac voltage of rms value 220 V at 50 Hz, so $T = 0.02$ s and $v_m = \sqrt2\times220 \approx 311$ V.
• The circuit symbol for an ac source is a circle with a sine wave inside it.

Identifying ac from a graph — a 1-mark favourite

• An alternating current must periodically reverse direction. Its $i$–$t$ graph is therefore symmetric about the time axis: equal positive and negative excursions, crossing zero repeatedly.
• A current that never becomes negative is unidirectional (dc), however much it varies with time. A rippled but always-positive line, a curve rising from a positive value and saturating, and a curve rising from the origin and saturating are all varying dc, not ac.
• Only a symmetric sinusoid oscillating between equal positive and negative values represents ac.

Why ac is preferred over dc

• AC voltages can be stepped up or stepped down easily and efficiently by means of a transformer. This is not possible with dc, because a transformer works by mutual induction and needs a changing flux.
• Because ac can be stepped up, electrical energy can be transmitted economically over long distances: at high voltage the current is small for the same power, so the $I^2R$ heating loss in the line is small.
• Most electrical energy sold by power companies is therefore generated, transmitted and distributed as ac, and most modern electrical devices are built to run on ac.

Points that the chapter builds on this

• Although the average of an alternating current over a complete cycle is zero, the average power dissipated is not zero: Joule heating depends on $i^2$, which is positive whether $i$ is positive or negative.
• AC circuits show phenomena dc circuits cannot — reactance, phase differences between voltage and current, and resonance. Resonance in a tuned LCR circuit is what lets a radio select one broadcasting station out of many.
• The convenience of ac is bought at the cost of a new bookkeeping: quantities must be handled as rms values, and voltages across different elements must be combined as phasors, not added arithmetically.